1+cosx是奇函数还是偶函数 怎么判断一个函数是奇函数还是偶函数
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2.\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0
3.\u5947\u51fd\u6570\u7684\u56fe\u50cf\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0
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5.\u82e5\u5947f(X)\u5728X=0\u5904\u6709\u5b9a\u4e49\uff0c\u5219f\uff080\uff09=0
\u5076\u51fd\u6570\uff1a1.\uff08\u4efb\u610f\uff09X \uff0cf(- X\uff09=f\uff08X\uff09
2.\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0
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2.\u6839\u636e\u5947\u5076\u51fd\u6570\u7684\u5b9a\u4e49\u6765\u5224\u65ad\uff1a\u518d\u5982f\uff08X\uff09=X\u76844\u6b21\u65b9\uff0c\u56e0\u4e3a\u5bf9\u5b9a\u4e49\u57df\u5185\u7684\u6bcf\u4e00\u4e2aX\uff0c\u90fd\u6709 f\uff08-X\uff09=\uff08-X\uff09\u76844\u6b21\u65b9=X\u76844\u6b21\u65b9=f\uff08X\uff09\uff0c\u8fd9\u5c31\u56de\u5230\u5b9a\u4e49\u4e0a\u6765\u770b\uff1a\u5076\u51fd\u6570\uff08\u4efb\u610f\uff09X \uff0cf(- X\uff09=f\uff08X\uff09
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\u82e5\u5bf9\u79f0\uff0cf(-x)=-f(x)\u7684\u662f\u5947\u51fd\u6570 f(-x)=f(x)\u7684\u662f\u5076\u51fd\u6570
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1.\u5982\u679c\u5bf9\u4e8e\u51fd\u6570\u5b9a\u4e49\u57df\u5185\u4efb\u610f\u4e00\u4e2ax\u90fd\u6709f(-x)=-(x)\uff0c
\u90a3\u4e48\u51fd\u6570f(x)\u5c31\u53eb\u505a\u5947\u51fd\u6570.
\u4f8b\u5982\uff1af(x)=x,
\u56e0\u4e3af(-x)=-x=-f(x),
\u6240\u4ee5f(x)=x\u662f\u5947\u51fd\u6570
2.\u5982\u679c\u5bf9\u4e8e\u51fd\u6570\u5b9a\u4e49\u57df\u5185\u4efb\u610f\u4e00\u4e2ax\u90fd\u6709f(-x)=f(x)\uff0c
\u90a3\u4e48\u51fd\u6570f(x)\u5c31\u53eb\u505a\u5076\u51fd\u6570.
\u4f8b\u5982:f(x)=x^2,
\u56e0\u4e3af(-x)=(-x)^2=x^2=f(x),
\u6240\u4ee5f(x)=x^2\u662f\u5076\u51fd\u6570
绛旓細鍋跺嚱鏁锛屽洜涓篺-x绛変簬fx
绛旓細cosx鏄伓鍑芥暟銆傛垜浠彲浠ユ牴鎹畒=cosx=cos锛-x锛夊彲浠ュ緱鍑烘槸鍋跺嚱鏁般傜浜屾垜浠彲浠ユ牴鎹甤osx鐨勫浘鍍忥紝cosx鐨勫浘鍍忔槸鍏充簬Y杞村绉帮紝鎵浠ュ彲浠ュ緱鍑篶osx鏄伓鍑芥暟銆傚鍑芥暟锛氬鏋滃嚱鏁癴锛坸锛夌殑瀹氫箟鍩熶腑浠绘剰x鏈塮锛-x锛=-f锛坸锛夛紝鍒欏嚱鏁癴锛坸锛夌О涓哄鍑芥暟銆傚伓鍑芥暟锛氬鏋滃嚱鏁癴锛坸锛夌殑瀹氫箟鍩熶腑浠绘剰x鏈塮锛-x锛=f锛...
绛旓細浣欏鸡鍑芥暟锛坹=cosx锛夋槸鍋跺嚱鏁銆傚鍑芥暟鏈夛細1銆佹寮﹀嚱鏁帮紙y=sinx锛夋槸濂囧嚱鏁般2銆佹鍒囧嚱鏁帮紙y=tanx锛夋槸濂囧嚱鏁般3銆佷綑鍒囧嚱鏁帮紙y=cotx锛夋槸濂囧嚱鏁般4銆佷綑鍓插嚱鏁帮紙y=cscx锛夋槸濂囧嚱鏁般傜浉鍏崇畝浠嬶細浣欏鸡=鍕鹃暱/寮﹂暱銆傚嬀鑲″鸡鏀惧埌鍦嗛噷銆傚鸡鏄渾鍛ㄤ笂涓ょ偣杩炵嚎銆傛渶澶х殑寮︽槸鐩村緞銆 鎶婄洿瑙掍笁瑙掑舰鐨勫鸡鏀惧湪鐩村緞涓婏紝鑲...
绛旓細鍋跺嚱鏁銆備竴鑸湴锛屽鏋滃浜庡嚱鏁癴x鐨勫畾涔夊煙鍐呬换鎰忕殑涓涓獂锛岄兘鏈塮x=f-x锛岄偅涔堝嚱鏁癴x灏卞彨鍋氬伓鍑芥暟EvenFunction銆傚叧浜庡師鐐瑰绉扮殑鍑芥暟鏄鍑芥暟锛屽叧浜嶻杞村绉扮殑鍑芥暟鏄伓鍑芥暟銆
绛旓細cosx鏄伓鍑芥暟銆傝鍒ゆ柇鍑芥暟y=cosx鏄鍑芥暟杩樻槸鍋跺嚱鏁般傛垜浠渶瑕佷簡瑙ｅ鍑芥暟鍜屽伓鍑芥暟鐨勫畾涔夈傚鍑芥暟鐨勫畾涔夋槸锛氬鏋滃浜庡嚱鏁癴锛坸锛夌殑瀹氫箟鍩熷唴鐨勪换鎰弜锛岄兘鏈塮锛−x锛=−f锛坸锛夛紝鍒欑Оf锛坸锛変负濂囧嚱鏁般傚伓鍑芥暟鐨勫畾涔夋槸锛氬鏋滃浜庡嚱鏁癴锛坸锛夌殑瀹氫箟鍩熷唴鐨勪换鎰弜锛岄兘鏈塮锛−x锛=f锛坸...
绛旓細cos x 鏄伓鍑芥暟,涓鏄鍑芥暟銆倅=cos x 鐨勫畾涔夊煙涓篟,鏍规嵁璇卞鍏紡,cos(-x)=cos x,鎵浠=cos x 鏄伓鍑芥暟銆傚叾鍥惧儚涓:
绛旓細1銆佸垎鏋愯繃绋嬪涓嬶細 鍋跺嚱鏁板畾涔夛細濡傛灉瀵逛簬鍑芥暟f (x)鐨勫畾涔夊煙鍐呬换鎰涓涓獂锛岄兘鏈塮 (-x)= f (x)锛岄偅涔堝嚱鏁癴 (x)灏卞彨鍋氬伓鍑芥暟銆 cos锛-x锛=cosx锛岀敱姝ゅ彲寰cosx鏄伓鍑芥暟銆2銆佸伓鍑芥暟瀹氫箟锛氬鏋滃浜庡嚱鏁癴(x)鐨勫畾涔夊煙鍐呬换鎰忎竴涓獂锛岄兘鏈塮(-x)= f(x)锛岄偅涔堝嚱鏁癴(x)灏卞彨鍋氬伓鍑芥暟銆濂囧嚱鏁瀹氫箟...
绛旓細浣欏鸡鍑芥暟锛坹=cosx锛鏄伓鍑芥暟 姝ｅ垏鍑芥暟锛坹=tanx锛鏄鍑芥暟 浣欏垏鍑芥暟锛坹=cotx锛夋槸濂囧嚱鏁 姝ｅ壊鍑芥暟锛坹=secx锛夋槸鍋跺嚱鏁 浣欏壊鍑芥暟锛坹=cscx锛夋槸濂囧嚱鏁 鍙渶璁颁綇姝ｅ鸡銆佷綑寮﹀嵆鍙紝鍏朵綑鍙帹寰椼倀anx=sinx/cosx 濂/鍋垛啋濂囧嚱鏁 cotx=cosx/sinx 鍋/濂団啋濂囧嚱鏁 secx=1/cosx 鍋跺嚱鏁 cscx=1/sinx 濂囧嚱鏁 ...
绛旓細sinx鏄鍑芥暟锛屽洜涓簊in(-x)=-sinx锛屽嵆褰撹嚜鍙橀噺鍙栫浉鍙嶆暟鏃讹紝鍑芥暟鍊间篃鍙栫浉鍙嶆暟銆cosx鏄伓鍑芥暟锛屽洜涓篶os(-x)=cosx锛屽嵆褰撹嚜鍙橀噺鍙栫浉鍙嶆暟鏃讹紝鍑芥暟鍊间笉鍙樸
绛旓細濂囧嚱鏁扮殑鍑芥暟鍥惧儚鏄叧浜庡師鐐瑰绉扮殑锛岃屽伓鍑芥暟鐨勫嚱鏁板浘鍍忔槸鍏充簬y杞村绉扮殑锛屽洜姝ゅ鏋滄兂瑕佸垎杈涓涓嚱鏁鏄鍑芥暟杩樻槸鍋跺嚱鏁锛屾垜浠彲浠ヤ粠璇ュ嚱鏁扮殑鍑芥暟鍥惧舰鐫鎵嬭繘琛屽垎鏋愩傚鍑芥暟鍦ㄥ叾瀵圭О鍖洪棿锛籥,b]鍜岋蓟锛峛锛岋紞a]涓婂叿鏈夌浉鍚岀殑鍗曡皟鎬э紝鍗冲凡鐭ユ槸濂囧嚱鏁帮紝瀹冨湪鍖洪棿锛籥,b]涓婃槸澧炲嚱鏁帮紙鍑忓嚱鏁帮級锛屽垯鍦ㄥ尯闂达蓟锛峛...
